A methodology to infer skin soil moisture from time series of passive microwave imagery is presented. Based on temporal changes in the microwave polarization difference temperature, it yields a quantitative moisture estimate as a fraction of field capacity. Based on a processing technique that separates low-frequency components caused by vegetation changes from fast precipitation-induced changes, its main feature is the complete independence of ground-based data. The method solely employs information contained in the microwave signal itself. When applied on Special Sensor Microwave/Imager imagery over the European continent, it is found that the methodology is only applicable to areas with sparse vegetation cover, where the fractional error (with respect to field capacity) is estimated to range from 16 to 28%. Finally, comparison of calculated moisture time series with observed precipitation shows a fair agreement.
 Owing to its control on the surface energy and water budgets, soil moisture has a significant influence on the atmosphere. At the continental scale, soil moisture plays a crucial role in soil-precipitation feedback mechanisms [Betts et al., 1996; De Ridder, 1997, 1998; Schär et al., 1999; Pielke, 2001]. At smaller scales, it affects near-surface meteorology and pollutant dispersion [Segal et al., 1990; Jacobson, 1999]. It is generally acknowledged that the correct representation of soil moisture in atmospheric models is a prerequisite for their accurate performance. However, one of the prohibiting factors in the improvement of land surface hydrology schemes is the lack of suitable validation data sets. Currently, only the ground-based Global Soil Moisture Data Bank [Robock et al., 2000] covers large enough space and timescales with sufficient sampling to be useful for the validation of large-scale models.
 As an alternative to ground-based measurements, satellite remote sensing in the microwave range constitutes a powerful complementary source of information. It relies on the fact that the dielectric constant of soils changes with water content, due to the alignment of the electric dipole of water molecules in response to an electromagnetic field, which in turn influences the soil's microwave polarization and emissivity characteristics. Microwave sensing is relatively unaffected by atmospheric water vapor and clouds, though cloud rainwater does affect the microwave signal at wavelengths on the order of a centimeter and smaller.
 In recent years, much progress has been made in deriving soil moisture from active microwave sensors such as the ERS-Scat and, more recently, the QuickScat scatterometers. Nevertheless, passive microwave imagers are of interest in soil moisture applications as the data produced by these types of instruments constitute a long time series. Indeed, together the Scanning Multichannel Microwave Radiometer (SMMR), the Special Sensor Microwave/Imager (SSM/I), and the recently launched Advanced Microwave Scanning Radiometer (AMSR) have been producing data spanning almost a quarter of a century.
 The focus of the present study is on the SSM/I, which has been aboard the polar platforms of the Defense Meteorological Satellite Program (DMSP) since 1987. Spanning more than 15 years at twice-daily temporal resolution, it provides global coverage. Although not designed for soil moisture sensing, the potential of the SSM/I to do so has been demonstrated in recent years. Heymsfield and Fulton  presented a detailed case study of the observed impact of rainfall and soil moisture on microwave brightness temperatures. They concluded that the SSM/I frequencies offer the possibility of gross monitoring of soil moisture in bare soil regions but much less so in vegetated areas. Teng et al.  found a strong correlation between 19.35 GHz horizontally polarized brightness temperature and the Antecedent Precipitation Index (API) over semiarid areas, the API being used as a proxy for soil moisture. They also concluded that for more densely vegetated areas, the correlation was not as good. Diak et al.  and Teng et al. , studying soil wetness in the context of the surface energy balance, pointed out that land surface fluxes could be characterized by a combination of remotely sensed soil moisture, and the Normalized Difference Vegetation Index (NDVI). Jackson  used actual surface moisture collected in a grassland region for the development and evaluation of different methods for estimating surface soil moisture from SSM/I data. He obtained the best agreement when normalizing horizontally polarized brightness temperatures with observed thermodynamic surface temperature to give emissivity, which was then used in a physically based model to calculate soil moisture. Lakshmi et al. [1997a] and Lakshmi  simulated soil moisture and microwave brightness temperatures by means of a coupled soil-canopy-atmosphere model and obtained reasonable correlations between simulated and SSM/I-based soil moisture. Felde  conducted a sensitivity study to quantify the effect of soil moisture on the 37 GHz polarization difference, i.e., the difference of the vertically and horizontally polarized brightness temperatures. He demonstrated that soil moisture information could be extracted from the polarization difference temperature (PDT) when the NDVI is used to account for the effect of vegetation. Recently, Vinnikov et al. [1999a] demonstrated that microwave emissivity and polarization difference at the SMMR's 18 GHz frequency have real utility for use as a soil moisture information source in regions where the vegetation is not too dense. Surprisingly, they also found that polarization difference correlated better with soil moisture at 18 GHz than at 6.6 GHz.
 Inspired by the overwhelming evidence of the usefulness of centimeter-wavelength passive microwave imagery for soil moisture sensing, a new methodology to retrieve quantitative estimates of the latter was proposed recently [De Ridder, 2000a]. Based on a physical model combined with a time series-processing scheme, it does not require any ground-based data, solely employing information contained in the satellite signal itself. This puts our scheme in the category of the so-called change-detection algorithms, which have proven to be very effective [see e.g., Wagner et al., 1999]. When applied to the site of the First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE) [Sellers et al., 1992] for a 2-week period in the summer of 1987, remotely sensed soil moisture and the associated simulated surface energy balance compared favorably to ground measurements [De Ridder, 2000a, 2000b].
 Whereas in De Ridder [2000a, 2000b] the model was applied to a small area and a short time period, the purpose of the present paper is to extend the methodology to continental-sized areas and seasonal timescales. The remainder of this article is organized as follows. In section 2, a brief overview of the method to infer skin soil moisture content from polarized microwave brightness temperature is given. In section 3, the method is applied to produce daily soil moisture maps over Europe for the period April–November 1990. Section 4 describes a detailed error analysis of the methodology, and in section 5, a selection of the results is shown. Appendix A gives a detailed description of the microwave emissivity model as a function of soil dielectric properties.
 The SSM/I is a seven-channel, four-frequency, linearly polarized, passive microwave radiometric system that measures brightness temperatures at 19.35, 22.235, 37.0, and 85.5 GHz. The sensing depth of the 19.35 GHz wave band, which is used here, is on the order of a few millimeters only [Engman and Chauhan, 1995]. The approximately 50-km effective spatial resolution of its 19.35 GHz channel is rather low, though sufficient in the context of regional or global climate modeling, since the horizontal scale of soil wetness, small-scale topography-related variability aside, extends over hundreds of kilometers [Vinnikov et al., 1999b; Entin et al., 2000].
 The above mentioned methodology [De Ridder, 2000a] derives quantitative soil moisture estimates from time series of the SSM/I PDT at 19.35 GHz. Combining existing theories and parameterizations, the PDT, defined as the difference between the vertically and horizontally polarized brightness temperatures, TV and TH, respectively, is expressed as (see Appendix A)
The left-hand side contains the specular surface microwave brightness temperature at vertical (subscript V) and horizontal (subscript H) polarization. The right-hand side contains the specular reflection coefficients at the air-soil boundary, ΓHsp and ΓVsp both functions of the volumetric soil moisture content m. These coefficients are computed using Fresnel's relations together with the model of Wang and Schmugge  for the moisture-dependent soil dielectric constant. The factor μ only contains parameters that do not depend on soil moisture directly:
The factor (1 − f) accounts for the portion of the SSM/I pixel that consists of bare soil; ta, Ts, and Td represent the microwave atmospheric transmissivity, the thermodynamic surface temperature, and the microwave downward atmospheric temperature, respectively. The parameters h and Q describe the microwave roughness and polarization mixing characteristics of the surface, respectively, as explained in Appendix A.
 If equation (1) were used as such, the specification of the external parameters appearing in μ, which are usually unknown at continental scales, would be required. Therefore the approach taken here is to use, for a given location, time series of the PDT, and to employ “changes” of the latter as an indication of soil moisture increase or decrease. More details of this technique are provided in the following section.
3. Data Processing
 The data employed, NOAA/NASA Pathfinder SSM/I Level 3 EASE-Grid Brightness Temperatures from the DMSP F8 platform, were obtained from the National Snow and Ice Data Center [National Snow and Ice Data Center (NSIDC), 1998]. These data are distributed as fields of radiometrically and geometrically calibrated brightness temperature on a 25-km grid. Ascending and descending passes of the DMSP platform normally produce data twice daily but, due to the limited swath width of 1400 km, some days have no data at all. As a consequence, 1–1.5 observations per day are available for a given pixel, on average. For the present study, fields of 19.35 GHz vertically and horizontally polarized brightness temperature were extracted from the NSIDC data set. The domain considered covers a large portion of Europe (Figure 1), and the period is April–November 1990.
 The processing scheme to retrieve soil moisture consists of the following three steps: (1) Smoothing, to reduce instrument-related noise and spurious signal components. (2) Construction of the so-called “wet” and “dry” curves, which represent envelope curves between which the PDT is scaled. (3) Application of equations (1) and (2), using the scaling established by the wet/dry curves, to convert PDT values to soil moisture content. Those three steps are now described in more detail below.
3.1. Spatiotemporal Smoothing
 First, the 19.35 GHz PDT fields are spatially smoothed by applying a running average using a 3 × 3 pixel spatial window. This has the effect of decreasing instrument-related noise, and it also reduces temporal changes that are induced by spatial gradients of surface dielectric characteristics combined with the geometric variability of the SSM/I field of view (more details are given below). A three-point running median filter is then applied to the PDT time series of each pixel, in order to remove outliers (spikes) due to instrument errors, or to the presence of perturbing factors such as small lakes appearing in the SSM/I's field of view. Furthermore, in order to remove cloud effects (which depress the PDT), a seven-point median filter acting solely on negative anomalies is applied. This filter replaces every point of the PDT time series by its running seven-point median but only if the latter is larger than the original value of the point considered. Using seven points effectively filters away negative anomalies extending over periods of 2–3 consecutive days.
3.2. Construction of Dry and Wet Curves
 A “running minimum” filter is then applied to produce the “dry curve,” defined as the values in the PDT time series that correspond to conditions of a dry upper soil. This filter yields, over a sliding interval of 21 points, the minimum occurring in it, which is then attributed to the central point. Note that the 21 points used in the filter cover 2–3 weeks on average; hence the dry curve contains only low-frequency components, which are mainly associated with seasonal changes in surface (f and Ts) and atmospheric (ta and Td) properties. In analogy, the “wet curve” corresponds to PDT values at conditions of field capacity. (The definition of field capacity used here is the soil moisture content corresponding to a hydraulic conductivity of 0.1 mm day−1.) The wet curve is computed theoretically from the dry curve using equation (1), as the ratio of the differences of the specular reflection coefficients for a soil at field capacity and a soil at zero moisture content (Figure 2), which amounts to multiplication by a factor of 1.72 in case of a silty clay loam soil.
 An example of the result of this processing sequence is displayed in the first panels of Figures 3a–3c, showing the filtered PDT together with the wet and dry curves. For ease of notation, the latter two will henceforth be referred to as PDTwet and PDTdry, respectively. Theoretically, all PDT values should fall between these enveloping curves, the example shown here satisfying this criterion reasonably well. However, it was also found that points in the domain sometimes exhibit PDT values larger than PDTwet. A possible explanation for such behavior is the occurrence of ponding water in all or a portion of the pixel considered. However, as our algorithm is not capable of dealing with such phenomena, it was decided to automatically set excess PDT values to PDTwet. Now from Figure 2 it can be seen that for moisture values above field capacity there is a saturation effect, in the sense that the polarization difference does not allow one to distinguish between, e.g., conditions at field capacity and at saturation. Therefore the consequence of imposing an upper limit on the PDT is that moisture retrieved with our algorithm has an upper limit at field capacity.
 A potentially problematical issue in the construction of the dry curve is that one cannot in principle be ensured that the soil becomes dry within any 3-week period, which is a prerequisite for the proper construction of this curve and, indeed, the functioning of the method. However, the moisture retrieved with our algorithm represents conditions at the upper few millimeters of the soil surface only, which very quickly becomes hydraulically decoupled from moisture at lower levels [Capehart and Carlson, 1997]. This means that, within a few days after heavy rain, the upper millimeters of soil may dry out almost completely, even if the upper 10 cm or so may remain relatively moist. Furthermore, as we exclude the winter season from our analysis, the evaporative demand of the atmosphere in the domain considered is high enough to make the complete drying out of the upper soil layers a reasonable assumption. In this context, it is important to notice that the DMSP F8 platform, from which data are used here, has equatorial crossing times of approximately 0615 and 1815 LT for the ascending and descending nodes, respectively. The latter crossing time is particularly useful for the construction of the dry curve, as it coincides very well with the time of day (toward sunset) when the probability of finding a dry upper soil is maximum. Furthermore, subsequent DMSP platforms (F11 and F13) are characterized by similar crossing times.
3.3. Soil Moisture Retrieval
 The basic idea behind the methodology is to scale processed PDT values between the dry and wet curves, such that the proximity of a point to either curve yields an indication of soil moisture status.
 Applying equations (1) and (2) for a completely dry soil, μ can be computed as
This means that no information regarding the parameters contained in the right-hand side of equation (2) is required to compute μ since the latter is obtained from the dry curve together with the difference of the polarized specular reflection coefficients for a completely dry soil, which is computed theoretically. Recalling that μ does not directly depend on soil wetness, equation (1) can be inverted to yield volumetric soil moisture content, using the observed values of the PDT together with μ as obtained in equation (3). Since the specular microwave reflectivities are not generally invertible in closed form, interpolation was used instead.
 In the computation of the specular microwave reflectivities, the specification of certain soil hydraulic parameters is required, which imposes choosing a soil textural type. The soil type chosen here is the silty clay loam soil from the United States Department of Agriculture (USDA) classification scheme, which can be considered an average soil type. Obviously, the whole of Europe does not consist of this type of soils. However, it was demonstrated [De Ridder, 2000a] that retrieved soil moisture exhibits relatively little sensitivity to soil texture. Also, in order to verify this earlier finding in the context of the present study, we applied the methodology for point number 1 (see Figure 1) using soil parameters for the 11 different textural types of the USDA classification scheme, ranging from very coarse (sand) to very fine (loam) textured soils. The 11 resulting curves are plotted together on the graph in Figure 4, confirming that our method exhibits relatively little sensitivity to soil texture. This is obviously a distinct advantage since textural maps are generally rather crude at the scale of continents and since spurious coregistration of soil maps and SSM/I imagery could easily lead to larger errors than those one would expect from assuming a single soil type for the entire domain.
3.4. Temporal Behavior of Parameters Involved
 As the processing scheme detailed above is largely based on temporal smoothing, it is important to be aware of the timescales over which the parameters in equation (2) vary. Indeed, the algorithm is based on the separability of short-term fluctuations caused by soil wetting from other, mainly slower, fluctuations. The vegetation cover f normally exhibits a seasonal cycle, and the soil parameters h and Q are, in principle, relatively steady over time. Therefore short-term fluctuations are not expected, except in case of human intervention such as harvesting or plowing. The temporal variability of the parameters ta, Ts, and Td, on the other hand, contains timescales similar to those characteristic of soil wetting, on the order of a day to several days. Hence the temporal variations of these parameters may interfere with the signal induced by soil moisture, leading to an error in the retrieval of the latter. However, as pointed out in the next section, the amplitude of the variations in the satellite signal caused by rapid fluctuations of ta, Ts, and Td are quite smaller than those induced by moisture variations.
 As far as the temporal variability of the dry and wet curves is concerned, the removal of fluctuations with timescales below a few weeks essentially leaves a signal characterized by the seasonal cycles of the vegetation cover f and the parameters ta, Ts, and Td.
4. Error Analysis
 As given by De Ridder [2000a], the error on the retrieved soil moisture content was shown to be
where δPDT is the error due to the instrument noise, δμ is the error due to fluctuations of atmospheric transmissivity and surface thermodynamic temperature, and s is the slope of the curve that relates the polarization difference reflectance to soil moisture. From Figure 2 it can be deduced that s ≈ 0.15/mfc. Based on instrument specifications, it was shown that δPDT is close to 0.59 K. Spatial averaging involving nine neighboring pixels (see previous section) reduces this error to δPDT ≈ 0.2 K. Since the PDT itself roughly varies between 5 and 50 K (see Figures 3a–3c), it follows that δPDT/PDT ≤ 0.04.
 In the analysis of the second term of equation (4), we only consider fluctuations occurring at timescales similar to those of moisture changes, i.e., a few days. The justification for doing so is that only these short-term fluctuations risk interference with the moisture-related fluctuations in the SSM/I signal. This means that we will assume that surface conditions (characterized by the parameters f, h, and Q) do not change over such short periods. As a result, we only need to consider fluctuations caused by the factor ta(Ts−Td) occurring in μ which, as shown by De Ridder [2000a], can be approximated as
Typical fluctuations on the order of 15 kg m−2 in the atmosphere's columnar water content yield δta/ta ≈ 0.07 [Choudhury, 1993]. Also, surface temperature fluctuations on the order of 20 K give δTs/Ts ≈ 0.07. Using these fluctuations with equation (5) in a standard error analysis then yields δμ/μ ≈ 0.12.
 Based on the above, the second term under the root of equation (4) is an order of magnitude larger than the first term. Ignoring the first term, and employing equation (1), the error on the retrieved moisture can thus be written as:
From Figure 2 it can be seen that ΓHsp − ΓVsp varies between approximately 0.21 and 0.35, meaning that the moisture content error varies between 16% (dry soils) and 28% (wet soils) of moisture at field capacity. This is close to what is generally accepted as minimally required for use as lower boundary condition in atmospheric models [Hall et al., 1995].
 As mentioned above, spatial smoothing was performed on the PDT signal in order to reduce the fluctuations caused by the geometric inaccuracy of the SSM/I. At the NSIDC, a gridding technique is applied to interpolate the brightness data on a predefined grid, called the Equal Area SSM/I Earth (EASE) grid. The weighting coefficients used in the interpolation depend on the orbital characteristics of the DMSP platform, and exhibit an 8-day periodicity (NSIDC, private communication, 1999). Although the gridding technique has been designed to preserve the original geometric accuracy to a maximal extent, it does not avoid the fact that the brightness temperature at a given location in the EASE grid corresponds to slightly different view areas each time. This means that, even if the surface microwave characteristics for a given area were to remain constant in time, the SSM/I signal may contain a time-dependent component, due to spatial gradients of surface properties combined with a changing field of view. This phenomenon has consequences for the method outlined above because it is based on temporal changes, making it inapplicable to appreciable parts of the domain. However, this perturbation exhibits a pronounced periodicity so that it can be recognized and filtered away.
 In the processing performed here, the PDT time series of each pixel was examined for the presence of a component with an 8-day period. In case this periodic component was too strong, which was decided on the basis of autocorrelation analysis, the pixel in question was discarded. Figure 5 shows an example of such an analysis, for a pixel where the 8-day periodicity is clearly visible in the time series itself (first panel) as well as in the autocorrelation analysis that exhibits peaks at lags of 8 days and multiples thereof (second panel). The stronger the peak at 8 days, the stronger the (spurious) periodicity; so we developed a criterion for the rejection of a pixel based on the strength of such a peak, requiring that the autocorrelation at day 8 should not exceed the minimum autocorrelation value occurring during days 1–7 by more than 0.05. The latter value was established empirically, as a balance between effectively discarding pixels exhibiting strong peaks at a lag of 8 days, while allowing for small (<0.05) fluctuations in the autocorrelation.
 Actually, for the domain and the period under consideration, 21.3% of the land pixels survived the rejection process and could be used to retrieve skin soil moisture. The areas where the method did work turn out to be those with a relatively high average PDT, which corresponds to the presence of significant fractions of bare soil in the field of view. This can be understood by looking at the fractional change of the PDT with changes in f, the vegetation cover fraction, alone. This fractional change can be calculated from equations (1) and (2), yielding
and showing that for lower values of f, the fractional change of the PDT exhibits less sensitivity to changes occurring in f (understood that those changes would be caused by a varying field of view).
 Finally, there are errors in the method that are associated with the effective temporal resolution of SSM/I measurements due to the appearance of clouds. Indeed, as clouds depress the signal, and as these depressions are filtered away by the processing scheme, the temporal resolution of the SSM/I measurements that are effectively available for the moisture retrieval algorithm may at times be limited to a few days. This often leads to a lag of the retrieved moisture by the same number of days, as will be apparent from the results shown in the following section.
 The results of the data processing described in section 3 consist of daily fields of skin soil moisture content derived for the domain shown in Figure 1, for the period covering Julian days 90–330 (April–November) of the year 1990. This excludes winter, when snow and frozen soils significantly perturb the SSM/I signal and make the moisture retrieval scheme inapplicable.
 As an example, Figure 6 displays soil moisture patterns in Europe for the period of 1–6 September 1990. A rigorous validation using measured volumetric moisture content was not possible due to the lack of suitable ground-truth data. As an alternative, moisture maps were compared with rainfall episodes, using daily precipitation amounts from the GEOS-1 Multiyear Assimilation [Schubert et al., 1993]. Though comparison of soil moisture with rainfall data has only limited value, a relation between heavy rainfall and subsequent SSM/I-derived moisture content can be observed. The passage of rain fronts leaves a signal in the German and Polish lowlands, where soil moisture is seen to increase suddenly. Note, however, that there is a slight time lag between the rainfall and the moisture increase, which is due to artifacts in the processing methodology as explained at the end of section 4.
 A more detailed confrontation of calculated moisture with observed rainfall is given in Figures 3a–3c, showing moisture time series for the three previously defined points (see Table 1 and Figure 1) together with station precipitation data contained in the Global Daily Summary data set, which was obtained from the National Climatic Data Center (U.S.). Figure 3a shows significant wetness episodes occurring at point 1 (Ukraine) around days 100, 115, 150, 165, and 310. All of these are also present in the precipitation time series. The latter also contains a significant peak at day 230 that is barely present in the moisture signal. However, this precipitation event occurred at only one of the two stations used in this validation, implying that surface wetting occurred over a limited portion of the SSM/I pixel, hence producing a weak signal. Again, a small lagging behind of the moisture signal with respect to the rainfall is observed.
Table 1. Details Regarding the Points Shown in Figure 1a
Model Grid Point
The columns under the heading “SSM/I-based data” describe the model grid points (identified as circles in Figure 1) for which soil moisture time series are studied in detail. The columns under the heading “station data” describe the corresponding meteorological stations (identified as cross symbols on Figure 1) of which precipitation data are used for the validation. Results of both type of points (grid and station) are shown in Figures 3a–3c.
Figure 3b shows moisture conditions at point 2 (Spain), with some modest wetting at the start of the considered period and more substantial wetting toward the end. The double rainfall peak occurring shortly after day 250 is nicely reproduced in the moisture signal. Also, the sustained wet period between days 290 and 320 corresponds well with the prolonged rain occurring during the same period. Only the major precipitation event around day 210 is not found in the moisture time series. Possible explanations are that antecedent moisture was probably very low owing to the extended dry period that preceded this event, and that this event occurred at the end of July, when hot and dry conditions could have led to very rapid reevaporation.
Figure 3c shows moisture conditions at point 3 (Libyan desert). The algorithm correctly reproduces the almost permanently dry conditions found in this area. The only major precipitation, which fell at the end of the considered period, scarcely produces a signal in the moisture time series, probably for the same reasons as those forwarded to explain the “missing” moisture peak for point 2 on day 210. An interesting observation is that the moisture fluctuations in Figure 3c exhibit a variability (“noise”) that is consistent with the previously estimated error of 20% with respect to field capacity.
 Again, we would like to stress the limited value of comparing moisture with rainfall episodes: indeed, skin moisture is determined by other factors, such as antecedent moisture content and evaporation. Especially skin moisture, representing conditions in the upper few millimeters of soil, is subject to rapid fluctuations. Nevertheless, most of the comparisons shown appear to suggest the validity of our approach.
 A methodology to obtain daily fields of skin soil moisture content from SSM/I 19.35 GHz brightness temperatures was briefly described and applied to Europe, for the period April–November 1990. Its main innovative character resides in the complete independence from ground-based measurements, which is achieved by a processing technique that is based exclusively on information contained in the satellite signal itself.
 A complete description of both the physical modeling and processing aspects of the scheme were provided, and an error analysis showed that the method is capable of yielding about five distinct levels of soil moisture between dry conditions and field capacity. When retrieved soil moisture time series were confronted with observed rainfall data a fair, though qualitative, agreement was found between both.
 In accordance with previous studies, it was found that centimeter-wavelength remote sensing is suitable for soil moisture retrieval, though in sparsely vegetated areas only. Despite this limitation, the skin soil moisture fields produced by our method have potential for the validation of regional climate simulations. The requirement of sparse vegetation cover together with the requirement that the upper millimeters of soil must become dry within any 3-week period, suggest that our approach would be mainly suited to arid regions or midlatitude areas with modest vegetation cover during summer. These are at the same time probably the areas that could benefit most from the approach presented here, as they have been identified in the past as having climates that exhibit a certain sensitivity to surface conditions, in particular soil moisture.
 The PDT is defined as
where T stands for the measured brightness temperature and the subscripts V and H refer to vertical and horizontal polarization, respectively. At terrestrial temperatures, the emitted microwave radiation is described by the Rayleigh-Jeans linear approximation of the Planck radiation law. Therefore in the case of a surface composed of patches of vegetation (percentage cover f) and bare soil, the PDT may be written as a linear combination of the soil temperatures of both surface types
The subscripts v and s refer to vegetation and bare soil, respectively. In equation (A2), use was made of the fact that for dense vegetation the PDT is approximately zero [Neale et al., 1990; Owe et al., 1992]. Clearly, the approach of subdividing the land surface into homogenous patches of dense vegetation interspersed with bare soil is a limitation of the methodology. Indeed, in many places on the globe sparse vegetation is present, meaning that there may be a contribution to the microwave signal stemming from microwave radiation emitted by the soil and subsequently transmitted through the sparse vegetation. However, Lakshmi et al. [1997b] showed that the actual distribution of vegetation (fully homogenous versus locally lumped) has a negligible influence on the PDT. Therefore it is reasonable to assume that our approach is applicable to mosaic-type as well as to sparsely vegetated landscapes.
 Taking into account atmospheric effects, the vertically and horizontally polarized brightness temperatures of the soil are given by Choudhury et al. 
In these expressions, Td and Tu are the effective downward and upward atmospheric temperatures, and ta is the atmospheric attenuation of the microwave signal, which is mainly influenced by water vapor. Ts is the thermodynamic temperature of the bare soil in the field of view of the SSM/I pixel and ΓV(H) is the microwave reflectivity at vertical (horizontal) polarization. Inserting equation (A3) in equation (A2) yields
 Not only the atmosphere but also the roughness characteristics of soils affect the measured brightness temperatures. Following Wang et al. , the surface microwave reflectivities are written using the specular reflectivities ΓVsp and ΓHsp together with two parameters that account for soil roughness effects
where Q is a depolarization factor and h is a frequency-dependent dimensionless number that characterizes soil roughness. Inserting these expressions in equation (A4) one obtains
The Fresnel equations [Ulaby et al., 1986] give the specular reflectivity of bare soils for vertical and horizontal polarizations:
 The satellite view angle θ is equal to 53° for the SSM/I and εs is the moisture-dependent complex dielectric constant of bare soil. The latter is parameterized as a function of the volumetric soil moisture content, denoted m, following the semiempirical model of Wang and Schmugge :
with m* = min(m,mt). The parameter msat is the soil moisture content at saturation, or the soil porosity. Defined this way, the dielectric constant of the soil exhibits two distinct regimes as a function of m depending on whether the latter is smaller or larger than the transition value ηt. The model contains two soil textural type-dependent coefficients: mt = 0.49 mwp + 0.165, and γ = −0.57 mwp + 0.481, and mwp is the soil moisture content at the wilting point. This parameter is defined as the moisture content corresponding to a water potential of −150 m, and exhibits lower values for coarser soils.
 The mixture model (A8) expresses the soil dielectric constant as a combination of air, solid soil, bound water, and free water contributions. The first three are given by εa = 1.0, εr = 5.5 − 0.2i, and εi = 3.2 − 0.1i, respectively, with i being the imaginary unit. The Debye relation gives the dielectric constant of water:
where ϕ is the frequency of the emitted radiation (here 19.35 GHz) and ϕ0 is the relaxation frequency of water at 23°C which is equal to 18.64 GHz. Above the freezing point, the dielectric constant of w ater exhibits a negligible dependence on temperature [Ulaby et al., 1986] so that ϕ0 is kept constant.
 SSM/I digital data were graciously provided by the NSIDC Distributed Active Archive Center, University of Colorado at Boulder. Precipitation data were obtained from the Distributed Active Archive Center at the Goddard Space Flight Center and the National Climatic Data Center.